Class 11

In a bulb factory, machines A, B and C manufactures 60 \%, 30 \% and 10 \% bulbs respectively. Out of these bulbs 1 \%, 2 \% and 3 \% of the bulbs produced respectively by A, B and C are found to be defective. A bulb is picked up at random from the total production and found to be defective. Find the probability that this bulb was produced by machine A.

Let $A$ : Manufactured from machine $A$, B : Manufactured from machine B C: Manufactured from machine C D : Defective bulb We want to find $P(A \mid D)$, i.e. probability of selected defective bulb...

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An insurance company insured 2000 scooters and 3000 motorcycles. The probability of an accident involving a scooter is 0.01, and that of motorcycles is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motorcycle.

Let $M$ : Motorcycle S: Scooter A : Accident vechicle We want to find $P(M \mid A)$, i.e. probability of accident vehicle was a motorcycle $\begin{array}{l} P(M \mid A)=\frac{P(M) \cdot P(A \mid...

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A car manufacturing factory has two plants X and Y. Plant X manufactures 70 \% of the cars, and plant Y, manufactures 30 \%. At pant X, 80 \% of the cars are rated of standard quality, and at plant Y, 90 \% are rated of standard quality. A car is picked up at random and is found to be of standard quality. A car is picked up at random and is found to be of standard quality. Find the probability that it has come from plant X.

Let $X$ : Car produced from plant $X$ $Y$ : Car produced from plant $Y$ S: Car rated as standard quality We want to find $P(X \mid S)$, i.e. selected standard quality car is from plant $X$...

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There are four boxes, A, B, C and D, containing marbles. A contains 1 red, 6 white and 3 black marbles; B contains 6 red, 2 white and 2 black marbles; C contains 8 red, 1 white and 1 black marbles; and D contains 6 white and 4 black marbles. One of the boxes is selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from the box A ?

Let $A:$ Ball drawn from bag $A$ B: Ball is drawn from bag B $C:$ Ball is drawn from bag $C$ $D:$ Ball is drawn from bag $D$ BB: Black ball WB : White ball RB : Red ball Assuming all boxes have an...

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There are 3 bags, each containing 5 white and 3 black balls. Also, there are 2 bags, each containing 2 white and 4 black balls. A white ball is drawn at random. Find the probability that this ball is from a bag of the first group.

Let $A$ : the set of first 3 bags $B$ : a set of next 2 bags WB : White ball BB : Black ball Now we can change the problem to two bags, i.e. bag A containing 15 white and 9 black balls( 5 white and...

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Urn A contains 7 white and 3 black balls; urn B contains 4 white and 6 black balls; urn C contains 2 white and 8 black balls. One of these urns is chosen at random with probabilities 0.2,0.6 and 0.2 respectively. From the chosen urn, two balls are drawn at random without replacement. Both the balls happen to be white. Find the probability that the balls are drawn are from urn C.

Let $A:$ Ball is drawn from bag $A$ B : Ball is drawn from bag B $C:$ Ball is drawn from bag $C$ BB: Black ball WB: White ball RB: Red ball Probability of picking 2 white balls fro urn $A=\frac{7...

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There are three boxes, the first one containing 1 white, 2 red and 3 black balls; the second one containing 2 white, 3 red and 1 black ball and the third one containing 3 white, 1 red and 2 black balls. A box is chosen at random, and from it, two balls are drawn at random. One ball is red and the other, white. What is the probability that they come from the second box?

let $A:$ Ball drawn from bag $A$ B : Ball is drawn from bag B $C:$ Ball is drawn from bag $C$ BB: Black ball WB: White ball RB: Red ball Assuming, selecting bags is of equal probability i.e....

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Three urns contain 2 white and 3 black balls; 3 white and 2 black balls, and 4 white and 1 black ball respectively. One ball is drawn from an urn chosen at random, and it was found to be white. Find the probability that it was drawn from the first urn.

let $\mathrm{A}:$ Ball drawn from bag $\mathrm{A}$ $B:$ Ball is drawn from bag $B$ $C:$ Ball is drawn from bag $C$ BB : Black ball WB : White ball Assuming, selecting bags is of equal probability...

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Three urns A, B and C contains 6 red and 4 white; 2 red and 6 white; and 1 red and 5 white balls respectively. An urn is chosen at random, and a ball is drawn. If the ball drawn is found to be red, find the probability that the balls was drawn from the first urn A.

let $A:$ Ball drawn from bag $A$ B : Ball is drawn from bag B $C:$ Ball is drawn from bag $C$ R: Red ball W : White ball Assuming, selecting bags is of equal probability i.e. $\frac{1}{3}$ We want...

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There are two I and II. The bag I contains 3 white and 4 black balls, and bag II contains 5 white and 6 black balls. One ball is drawn at random from one of the bags and is found to be white. Find the probability that it was drawn from the bag I.

Let $\mathrm{W}$ : White ball B : Black ball $\begin{array}{l} X: 1^{\text {st }} \text { bag } \\ Y: 2^{\text {nd }} \text { bag } \end{array}$ Assuming, selecting bags is of equal probability i.e....

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A bag A contains 1 white and 6 red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag A. red balls. Another bag contains 4 white and 3 red balls. One of the bags is selected at random, and a ball is drawn from it, which is found to be white. Find the probability that the ball is drawn is from bag A.

Let R : Red ball W : White ball A: Bag A B: Bag B Assuming, selecting bags is of equal probability i.e. $\frac{1}{2}$ We want to find $P(A \mid W)$, i.e. the selected white ball is from bag $A$:...

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Two groups are competing for the positions on the board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4, respectively. Further, if the first group wins, the probability of introducing a new product is 0.7, and when the second groups win, the corresponding probability is 0.3. Find the probability that the new product introduced was by the second group.

Let $F$ : First group S : Second group $N$ : Introducing a new product We want to find $P(S \mid N)$, i.e. new product introduced by the second group $\begin{array}{l} \mathrm{P}(\mathrm{S} \mid...

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